Tangent Spaces and Submersions

Related lectures (28)

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Explores norms, orthogonality, and the Pythagorean theorem in vector spaces.

Covers kernels and images of linear transformations between vector spaces, illustrating properties and providing proofs.

Covers the concept of orthogonal complement in Rn and related propositions and theorems.

Explores vector subspaces and linear combinations in linear algebra, focusing on the reciprocal relationship between lines, columns, and elements.

Covers strategies for matrix operations and the concept of vector spaces.

Explores bases, dimensions, and matrix ranks in vector spaces with practical examples and proofs.

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Explores orthogonality, norms, and distances in vector spaces for solving linear systems.

Explains kernel, image, and linear maps, illustrating concepts with examples.

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.